Đáp án:
Giải thích các bước giải:
`B = 2/3 - 2/3^2 + 2/3^3 -...........+ 2/3^99 - 2/3^100`
`B = 2 . ( 1/3 - 1/3^2 + 1/3^3 -..............+ 1/3^99 - 1/3^100 )`
-Đặt `D = 1/3 - 1/3^2 + 1/3^3 -..............+ 1/3^99 - 1/3^100`
`3D = 1 - 1/3 + 1/3^2 -............+ 1/3^98 - 1/3^99`
`3D + D = ( 1 - 1/3 + 1/3^2 -............+ 1/3^98 - 1/3^99 ) + ( 1/3 - 1/3^2 + 1/3^3 -..............+ 1/3^99 - 1/3^100 )`
`4D = 1 - 1/3^100`
`D = 1/4 - 1/(3^100 . 4)`
`→ B = 2 . ( 1/4 - 1/(3^100 . 4) )`
`→ B = 1/2 - 1/(3^100 . 2)`
